What is the Formula for ln ex/ex?

[JasonX]

[SOLVED] need formula or how to...

y= ln ex/ex (x is the power)

 

[rock.freak667]

uhm use the "^" to represent powers, for example, x squared is written as x^2

and please state your question better

 

[JasonX]

uhm use the "^" to represent powers, for example, x squared is written as x^2

and please state your question better

Differentiate:

y= ln e^x/e^x


Thanks!

 

[rock.freak667]

So the question is to differentiate

$$y=\frac{ln e^x}{e^x}$$ ?


if it is...what rule do you think you would use when you need to differentiate something of the form $y=\frac{u}{v}$ ?

 

[JasonX]

quotient rule.
which is: first, derivative of second, minus second, derivative of first, divided by first squared. (but, I'm still stuck. could you work it out for me?)

 

[rock.freak667]

Well firstly...lne^x can be simplified to xlne which is just x

so you really want to find $$\frac{d}{dx}(\frac{x}{e^x})$$

so if u= x => $\frac{du}{dx}=1$
and v=e^x => $\frac{dv}{dx}=e^x$

the formula is
$$\frac{d}{dx}(\frac{u}{v}) =\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}$$so then you'll have
$$\frac{d}{dx}(\frac{x}{e^x}) = \frac{(e^x)(1) -(x)(e^x)}{(e^x)^2}$$

then you will simplify it

 

[JasonX]

thanks a lot. you made it very easy to understand. only part i didn't get is it says answer should be 1-x/e^x. what cancels out the power in the denominator?


Thanks again!

 

[rock.freak667]

...well the e^x in the numerator can be factored out and it will cancel with an e^x in the denominator...so giving you your answer

 

[JasonX]

oh, i see. thank you very much.. :)